Transcript What is this measurement?

Chapter 1B
Measurement
1
CHAPTER OUTLINE
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SI Units
Scientific Notation
Error in Measurements
Significant Figures
Rounding Off Numbers
Conversion of Factors
Conversion of Units
Volume & Density
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SI UNITS
 Measurements are made by scientists to
determine size, length and other properties of
matter.
 For measurements to be useful, a measurement
standard must be used.
 A standard is an exact quantity that people agree
to use for comparison.
 SI is the standard system of measurement used
worldwide by scientists.
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SI BASE UNITS
Quantity Measured
Units
Symbol
Meter
m
Mass
Kilogram
kg
Time
Seconds
s
Kelvin
K
Mole
mol
Electric current
Ampere
A
Intensity of light
Candela
cd
Length
Temperature
Amount of substance
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DERIVED UNITS
 In addition to the base units, several derived
units are commonly used in SI system.
Quantity Measured
Units
Symbol
Volume
Liter
L
Density
grams/cc
g/cm3
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SCIENCTIFIC
NOTATION
 Scientific Notation is a convenient way to express
very large or very small quantities.
 Its general form is
A x 10n
coefficient
n = integer
1  A < 10
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SCIENTIFIC
NOTATION
To convert from decimal to scientific notation:
Move the
point by
in the
original number
 Follow
thedecimal
new number
a multiplication
signso
that 10
it iswith
located
after the(power).
first nonzero digit.
and
an exponent
 The exponent is equal to the number of places that
the decimal point was shifted.
75000000
7.5 x 10 7
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SCIENTIFIC
NOTATION
 For numbers smaller than 1, the decimal moves
to the left and the power becomes negative.
0 00642
6.42 x 10
3
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Examples:
1. Write 6419 in scientific notation.
decimal after
first nonzero
digit
power of 10
64.19x10
641.9x10
6419.
6419
6.419
x 10213
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Examples:
2. Write 0.000654 in scientific notation.
decimal after
first nonzero
digit
power of 10
-1
-2
-3
-4
0.000654
0.00654
x
10
0.0654
0.654
10
6.54 xx10
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CALCULATIONS WITH
SCIENTIFIC NOTATION
 To perform multiplication or division with
scientific notation:
1. Change numbers to exponential form.
2. Multiply or divide coefficients.
3. Add exponents if multiplying, or subtract
exponents if dividing.
4. If needed, reconstruct answer in standard
exponential form.
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Example 1:
Multiply 30,000 by 600,000
Convert
Multiply
Reconstruct
Add
to exponential
exponents
coefficients
answerform
(3 x 104) (6 x 105) = 18 x 10 9
1.8 x 1010
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Example 2:
Divided 30,000 by 0.006
Convert
Subtract
Reconstruct
Divide
to exponential
coefficients
exponents
answerform
4 – (-3)
(3 x 104)
(6 x 10-3)
= 0.5 x 10
7
5 x 106
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Follow-up Problems:
(5.5x103)(3.1x105) = 17.05x108 = 1.7x109
(9.7x1014)(4.3x1020) = 41.71x106
= 4.2x105
6
2.6x10
4
0.4483x10
=
5.8x102
1.7x10
8.2x10
= 4.5x103
5
8
= 0.2073x103
= 2.1x102
(3.7x106)(4.0x108) = 14.8x102 = 1.5x103
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Follow-up Problems:
(8.75x1014)(3.6x108) = 31.5x1022 = 3.2x1023
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1.48x10
41
=
0.2041x10
7.25x1013
= 2.04x1042
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ERROR IN
MEASUREMENTS
 Two kinds of numbers are used in science:
Counted or defined:
exact numbers; have no uncertainty
Measured:
are subject to error; have uncertainty
 Every measurement has uncertainty because of
instrument limitations and human error.
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ERROR IN
MEASUREMENTS
certain
certain
8.65
8.6
uncertain
uncertain

What
Theislast
thisdigit
measurement?
in any
measurement
is the
What
is this measurement?
estimated one.
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SIGNIFICANT
FIGURES RULES
1. Significant
figures
figures
are
arecertain
used toand
determine
uncertain
All non-zero
digitsrules
arethe
significant.
which
digits in
digits
a measurement.
are significant and which are not.
2. All sandwiched zeros are significant.
3. Leading zeros (before or after a decimal) are
NOT significant.
4. Trailing zeros (after a decimal) are significant.
0
.
0
0
4
0
0
4
5
0
0
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Examples:
Determine the number of significant figures in each
of the following measurements.
461 cm
3 sig figs
1025 g
4 sig figs
0.705 mL
3 sig figs
93.500 g
5 sig figs
0.006 m
1 sig fig
5500 km
2 sig figs
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ROUNDING OFF
NUMBERS
 If rounded digit is less than 5, the digit is dropped.
51.234
Round to 3 sig figs
1.875377
Less than 5Round
to 4 sig figs
Less than 5
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ROUNDING OFF
NUMBERS
 If rounded digit is equal to or more than 5, the
digit is increased by 1.
4
51.369
Round to 3 sig figs
1
5.4505
More than Round
5
to 4 sig figs
Equal to 5
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SIGNIFICANT
FIGURES & CALCULATIONS
 The results of a calculation cannot be more
precise than the least precise measurement.
 In multiplication or division, the answer must
contain the same number of significant figures
as in the measurement that has the least number
of significant figures.
 For addition and subtraction, the answer must
have the same number of decimal places as
there are in the measurement with the fewest
decimal places.
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MULTIPLICATION
& DIVISION
3 sig figs
4 sig figs
Calculator
answer
(9.2)(6.80)(0.3744) = 23.4225
2 sig figs
The answer should have two significant
figures because 9.2 is the number with
the fewest significant figures.
The correct answer is 23
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ADDITION &
SUBTRACTION
Add 83.5 and 23.28
Least precise number
Calculator
answer
Correct answer
83.5
23.28
106.78
106.8
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Example 1:
5.008 + 16.2 + 13.48 = 34.688
34.7
Least precise
number
Round to
25
Example 2:
3 sig figs
3.15 x 1.53
= 6.1788
0.78
6.2
2 sig figs
Round to
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SI PREFIXES
 The
Common
SI system
prefixes
of units
are
used
is easy
with
to the
use base
because
units
it is
to
SI Prefixes
indicate
multiple
ten that the unit represents.
based onthe
multiples
ofof
ten.
Prefixes
mega-
Symbol
M
kilocentimilli-
k
c
m
micro-

Multiplying factor
1,000,000
106
1000
103
0.01
10-2
0.001
10-3
0.000,001 10-6
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SI PREFIXES
How many cm
mmare
areininaakm?
cm?
100000
10x10x10x10x10
10
or 105
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CONVERSION
FACTORS
 Many problems in chemistry and related fields
require a change of units.
 Any unit can be converted into another by use of
the appropriate conversion factor.
 Any equality in units can be written inMetric-Metric
the form of a
Factor
fraction called a conversion factor. For example:
Equality
Conversion Factors
1 m = 100 cm
1m
100 cm
or
100 cm
1m
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CONVERSION
FACTORS Metric-English
Factor
Equality
1 kg = 2.20 lb
Conversion Factors
1 kg
2.20 lb
or
2.20 lb
1 kg
 Sometimes a conversion factor is given Percentage
as a percentage.
For example:
Factor
Percent quantity:
Conversion
Factors
18% body fat by mass
18 kg body fat
100 kg body mass
or
100 kg body mass
18 kg body fat
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CONVERSION
OF UNITS
 Problems involving conversion of units and other
chemistry problems can be solved using the
following step-wise method:
4.
2.
3.
Write
Set
Planupathe
the
sequence
conversion
problem
of steps
by
factor
arranging
to convert
forand
each
cancelling
the
units
initial
change
units
unit
in
in
tothe
the
1. Determine
the
intial
unit
given
the
final
unit
needed.
final unit.
your
numerator
plan. and denominator of the steps involved.
beginning unit x
final unit
= final unit
beginning unit
Conversion factor
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Example 1:
Convert 164 lb to kg (1 kg = 2.20 lb)
Step 1:
Step 2:
Step 3:
Step 4:
Given: 164 lb
lb
1 kg
2.20 lb
Need: kg
English-Metric
factor
or
kg
2.20 lb
1 kg
1 kg
164 lb x
= 74.5 kg
2.20 lb
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Example 2:
The thickness of a book is 2.5 cm. What is this measurement
in mm?
Step 1:
Given: 2.5 cm
Step 2:
cm
Step 3:
1 cm
10 mm
Step 4:
Need: mm
Metric-Metric
factor
or
mm
10 mm
1 cm
10 mm
2.5 cm x
= 25 mm
1 cm
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Example 3:
How many centimeters are in 2.0 ft? (1 in=2.54 cm)
Step 1:
Given: 2.0 ft
Step 2:
ft
Step 3:
Step 4:
English-English
factor
1 ft
12 in
and
Need: cm
in
English-Metric
factor
cm
1 in
2.54 cm
12 in 2.54 cm
61 cm
cm
2.0 ft x
x
= 60.96
1 ft
1 in
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Example 4:
Bronze is 80.0% by mass copper and 20.0% by mass tin.
A sculptor is preparing to case a figure that requires
1.75 lb of bronze. How many grams of copper are
needed for the brass figure?
Step 1:
Step 2:
Given: 1.75 lb bronze
lb
brz
English-Metric
factor
g
brz
Need: g of copper
Percentage
factor
g
Cu
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Example 4:
Step 3:
Step 4:
1 lb
454 g
1.75 lb brz x
and
454 g
1 lb
80.0 g Cu
100 g brz
80.0 g Cu
x
==
635.6
636 g
100 g brz
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VOLUME
 Volume is the amount of space an object
occupies.
 Common units are cm3 or liter (L) and
milliliter (mL).
1 L = 1000 mL
1 mL = 1 cm3
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DENSITY
 Density is mass per unit volume of a material.
 Common units are g/cm3 (solids) or g/mL (liquids).
Densityis isindirectly
directly
Density
proportionaltotothe
the
proportional
mass of
volume
ofan
anobject.
object.
Which has greatest density?
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Example 1:
A copper sample has a mass of 44.65 g and a volume
of 5.0 cm3. What is the density of copper?
m = 44.65 g
V = 5.0
cm3
d=
m
V
=
44.65 g
5.0 mL
= 8.9
8.93g/cm
g/cm3 3
d = ???
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Example 2:
A silver bar with a volume of 28.0 cm3 has a mass of
294 g. What is the density of this bar?
m = 294 g
V = 28.0
cm3
d=
m
V
=
294 g
28.0 mL
= 10.5 g/cm3
d = ???
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Example 3:
If the density of gold is 19.3 g/cm3 , how many grams
does a 5.00 cm3 nugget weigh?
Step 1:
Given: 5.00 cm3
Step 2:
cm3
Step 3:
19.3 g
1 cm3
Step 4:
Need: g
density
or
g
1 cm3
19.3 g
19.3 g
5.00 cm x
= 96.5 g
3
1 cm
3
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Example 4:
If the density of milk is 1.04 g/mL, what is the mass
of 0.50 qt of milk? (1L = 1.06 qt)
Step 1:
Given: 0.5 gt
English-metric
Factor
Step 2:
qt
Step 3:
1000
1LmL
1.06 qt
Step 4:
and
Need: g
mL
density
g
1.04 g
1 mL
1000 mL 1.04 g
x
0.50 qt x
= 490
490.57
g g
1 mL
1.06 qt
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Example 5:
What volume of mercury has a mass of 60.0 g if its
density is 13.6 g/mL?
1 mL
4.41 mL
=
60.0 g x
13.6 g
inverse of
density
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DENSITY & FLOATING
 Objects float in liquids
when their density is
lower relative to the
density of the liquid.
 The density column
shown was prepared by
layering liquids of
various densities.
 See demo
less dense
Isopropyl alcohol
Vegetable oil
Water
Soap
Syrup
more dense
Honey
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IS UNIT CONVERSION
IMPORTANT?
 Further
In 1999 Mars
Climateshowed

investigation
orbiter
was lostatinLockheed
space
that
engineers
because which
engineers
Martin,
builtfailed
the to
make a simple
conversion
aircraft,
calculated
from Englishmeasurements
units to
navigational
in
metric, an
embarrassing
English
units.
When NASA’s
lapseengineers
that sent received
the $125the
JPL
million
craft
fatallythe
close to
data,
they
assumed
the Martian was
surface.
information
in metric
units, causing the confusion.
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THE END
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